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 Rising water levels (Posted on 2006-06-26)
You have rectangular pot of water 10cm by 10cm at the bottom and 6 cm deep. It is filled to a depth of 3cm.

You have 7 solid steel shapes in front of you. The question is to find the new level of the water after each shape is put in the pot in the orientation described. The previous shape is removed before adding the next.

1. A cube 5cm on a side.

2. A prism in the shape of a right triangle with legs 5cm long. It is 5cm high but is placed on one of its legs with its hypotenuse sloping out of the water.

3. Another prism, this one having an equilateral triangle of sides 5cm and height 5cm. It is to be placed on its side with two faces sloping up out of the water.

4. A regular hexagonal prism. Each edge of the hexagon is 4cm and the height is 5cm. It is to be placed on its side.

5. A right square pyramid. Its base is 6cm on a side. It is 5cm high. It is to be placed base down.

6. A right cylinder of radius 3cm and length 5cm. It is to be placed on its side.

7a. A right cone of radius 3cm and height 5cm. It is to be placed base down.

7b. The same cone as 7a. This time placed on its side.

 No Solution Yet Submitted by Jer Rating: 4.1667 (6 votes)

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 Excellent problem! #1 solved | Comment 6 of 26 |

This is a wonderful problem, Jer.  Not too easy, not too hard.  Just challenging enough to make it interesting.

As I work my way through them, each one seems more difficult than the last.

#1 was easy to solve:  The water level in the tank would be 4cm.

The square tank has a floor surface area of 10cm x 10cm = 100cm2.   At 3cm deep, the total volume of water is 300cm3.    A square cube 5cm on a side covers 25cm2 of the floor surface, reducing the equivalent surface area to 75cm2. Now, the 300cm of water fills the tank up to the 4cm level (4 x 75 = 300).

 Posted by Mindrod on 2006-06-28 00:52:27

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